scholarly journals Path-integral approximation on the stability of large bipolarons in quasi-one-dimensional confinement

2000 ◽  
Vol 61 (9) ◽  
pp. 6063-6068 ◽  
Author(s):  
R. T. Senger ◽  
A. Erçelebi
Keyword(s):  
Path Integral ◽  
Integral Approximation ◽  
One Dimensional ◽  
The Stability

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Stability of a one-dimensional morphoelastic model for post-burn contraction

2021 ◽  
Vol 83 (3) ◽  
Author(s):  
Ginger Egberts ◽  
Fred Vermolen ◽  
Paul van Zuijlen
Keyword(s):  
Wound Healing ◽  
Residual Stresses ◽  
Truncation Error ◽  
Signaling Molecules ◽  
Discrete Problem ◽  
One Dimensional ◽  
Stability Constraint ◽  
Biological Interpretation ◽  
The Stability ◽  
The One

AbstractTo deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order $${{\mathcal {O}}}(h^2)$$ O ( h 2 ) . Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

scholarly journals One-Dimensional Organic–Inorganic Material (C6H9N2)2BiCl5: From Synthesis to Structural, Spectroscopic, and Electronic Characterizations

2021 ◽  
Vol 22 (4) ◽  
pp. 2030
Author(s):  
Hela Ferjani ◽  
Hammouda Chebbi ◽  
Mohammed Fettouhi
Keyword(s):  
Hydrogen Bonding ◽  
Density Functional ◽  
Crystal Packing ◽  
Diffuse Reflectance Spectrum ◽  
Enrichment Ratio ◽  
One Dimensional ◽  
Organic Part ◽  
Fukui Indices ◽  
The Stability ◽  
The One

The new organic–inorganic compound (C6H9N2)2BiCl5 (I) has been grown by the solvent evaporation method. The one-dimensional (1D) structure of the allylimidazolium chlorobismuthate (I) has been determined by single crystal X-ray diffraction. It crystallizes in the centrosymmetric space group C2/c and consists of 1-allylimidazolium cations and (1D) chains of the anion BiCl52−, built up of corner-sharing [BiCl63−] octahedra which are interconnected by means of hydrogen bonding contacts N/C–H⋯Cl. The intermolecular interactions were quantified using Hirshfeld surface analysis and the enrichment ratio established that the most important role in the stability of the crystal structure was provided by hydrogen bonding and H···H interactions. The highest value of E was calculated for the contact N⋯C (6.87) followed by C⋯C (2.85) and Bi⋯Cl (2.43). These contacts were favored and made the main contribution to the crystal packing. The vibrational modes were identified and assigned by infrared and Raman spectroscopy. The optical band gap (Eg = 3.26 eV) was calculated from the diffuse reflectance spectrum and showed that we can consider the material as a semiconductor. The density functional theory (DFT) has been used to determine the calculated gap, which was about 3.73 eV, and to explain the electronic structure of the title compound, its optical properties, and the stability of the organic part by the calculation of HOMO and LUMO energy and the Fukui indices.

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

FUNCTIONAL INTEGRALS AND PHASE STRUCTURES IN SINE-GORDON–THIRRING MODEL

2012 ◽  
Vol 26 (27) ◽  
pp. 1250178 ◽  
Author(s):  
JUN YAN
Keyword(s):  
Strong Coupling ◽  
Finite Temperature ◽  
Thirring Model ◽  
Attractive Potential ◽  
Functional Integrals ◽  
One Dimensional ◽  
Phase Structures ◽  
Coexistence Phase ◽  
Coupling Case ◽  
The Stability

The phase structures of one-dimensional quantum sine-Gordon–Thirring model with N-impurities coupling are studied in this paper. The effective actions at finite temperature are derived by means of the perturbation and non-perturbation functional integrals method. The stability of coexistence phase is analyzed respectively in the weak and strong coupling case. It is shown that the coexistence phase is not stable when fermions have an attractive potential g < 0, and the stable coexistence phase can form when fermions have an exclude potential g > 0.

Sensitivity Analysis and Numerical Stability Analysis of the Algorithms for Predicting the Performance of Turbines

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Ming Wei ◽  
Yonghong Wang ◽  
Huafen Song
Keyword(s):  
Numerical Stability ◽  
Rounding Error ◽  
One Dimensional ◽  
Flow Models ◽  
Numerical Stability Analysis ◽  
Last Stage ◽  
The Stability ◽  
Performance Calculation ◽  
Poor Stability ◽  
Input Error

Sensitivity and numerical stability of an algorithm are two of the most important criteria to evaluate its performance. For all published turbine flow models, except Wang method, can be named the “top-down” method (TDM) in which the performance of turbines is calculated from the first stage to the last stage row by row; only Wang method originally proposed by Yonghong Wang can be named the “bottom-up” method (BUM) in which the performance of turbines is calculated from the last stage to the first stage row by row. To find the reason why the stability of the two methods is of great difference, the Wang flow model is researched. The model readily applies to TDM and BUM. How the stability of the two algorithms affected by input error and rounding error is analyzed, the error propagation and distribution in the two methods are obtained. In order to explain the problem more intuitively, the stability of the two methods is described by geometrical ideas. To compare with the known data, the performance of a particular type of turbine is calculated through a series of procedures based on the two algorithms. The results are as follows. The more the calculating point approaches the critical point, the poorer the stability of TDM is. The poor stability can even cause failure in the calculation of TDM. However, BUM has not only good stability but also high accuracy. The result provides an accurate and reliable method (BUM) for estimating the performance of turbines, and it can apply to all one-dimensional performance calculation method for turbine.

Stability Considerations in Thermoelastic Contact

1980 ◽  
Vol 47 (4) ◽  
pp. 871-874 ◽  
Author(s):  
J. R. Barber ◽  
J. Dundurs ◽  
M. Comninou
Keyword(s):  
Steady State ◽  
Perturbation Method ◽  
Energy Function ◽  
First Principles ◽  
Dimensional Model ◽  
Contact Conditions ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
The Stability ◽  
Steady State Solutions

A simple one-dimensional model is described in which thermoelastic contact conditions give rise to nonuniqueness of solution. The stability of the various steady-state solutions discovered is investigated using a perturbation method. The results can be expressed in terms of the minimization of a certain energy function, but the authors have so far been unable to justify the use of such a function from first principles in view of the nonconservative nature of the system.

Stability of Viscoelastic Channel Flow

2007 ◽  
Author(s):  
Nariman Ashrafi
Keyword(s):  
Reynolds Number ◽  
Viscosity Ratio ◽  
Weissenberg Number ◽  
Base Flow ◽  
Galerkin Projection ◽  
Large Reynolds Number ◽  
One Dimensional ◽  
Stress Effects ◽  
The Stability ◽  
The One

The nonlinear stability and bifurcation of the one-dimensional channel (Poiseuille) flow is examined for a Johnson-Segalman fluid. The velocity and stress are represented by orthonormal functions in the transverse direction to the flow. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. The stability picture is dramatically influenced by the viscosity ratio. The range of shear rate or Weissenberg number for which the base flow is unstable increases from zero as the fluid deviates from the Newtonian limit as decreases. Typically, two turning points are observed near the critical Weissenberg numbers. The transient response is heavily influenced by the level of inertia. It is found that the flow responds oscillatorily. When the Reynolds number is small, and monotonically at large Reynolds number when elastic effects are dominated by inertia.

scholarly journals Synthesis and characterization of one-dimensional titanate structure

2008 ◽  
Vol 2 (2) ◽  
pp. 109-114 ◽  
Author(s):  
Ljubica Nikolic ◽  
Marija Maletin ◽  
Paula Ferreira ◽  
Paula Vilarinho
Keyword(s):  
Heat Treatment ◽  
Structural Characteristics ◽  
Hydrothermal Process ◽  
Synthesis And Characterization ◽  
One Dimensional ◽  
Treatment Conditions ◽  
Alkaline Conditions ◽  
The Stability ◽  
Simple Hydrothermal Process

One-dimensional titania structures were synthesized trough a simple hydrothermal process in a highly alkaline conditions. The aim of this work was to elucidate the effect of time on the formation of 1D titanates as well on its structural characteristics (morphology, phase composition, surface area). Apart from that, the effect of heat treatment conditions on the stability of titanate based 1D samples has been investigated. The results have revealed that it is possible to form one-dimensional titanates already after 1 hour of hydrothermal synthesis. Although the composition of titanates is still under debate, the results probably correspond to the layered sodium titanates. The 1D prepared structures show a remarkable stability during heating, remaining the basic morphology and composition even up to 700?C.

Sign in / Sign up

Export Citation Format

Share Document